Free vibrations of a tire as a toroidal membrane

S. Saigal, T. Y. Yang, H. W. Kim, W. Soedel

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42 Scopus citations


A tire is modeled as a toroidal membrane under internal pressure and mounted on a rim, to investigate its free vibration characteristics using a 12 d.o.f. rectangular membrane finite element. Such a modeling is valid if the tire is assumed to be incapable of supporting any weight in the absence of internal pressure. To verify the formulations of the membrane finite element, a flat rectangular membrane subject to in-plane loads and a circular cylindrical membrane under internal pressure are first analyzed. Analytical solutions for these cases are also derived. The analytical and numerical results are in good agreement. A toroidal membrane under internal pressure, assumed to model a low pressure tire, is studied next. Both the analytical derivation and the finite element solutions are presented. For the analytical solution the equations of motion yield a complicated differential equation for which an approximate solution is obtained by assuming that the parallel circle radius is constant as in the case of a bycycle wheel. The finite element solution successfully predicts the symmetrical and the twisting modes of vibration documented by other researchers, and is also in good agreement with the analytical results. The present formulations are useful to obtain a good first approximation of the free vibration response of a tire.

Original languageEnglish (US)
Pages (from-to)71-82
Number of pages12
JournalJournal of Sound and Vibration
Issue number1
StatePublished - May 22 1986
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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